From movie London (2005)
A going-away party. A girl named London is gonna leave from the town. A lot of people are at the party. One of the girls says to London.
- Girl: Hey, girl, I'm out of here.
- London: Already?
- Girl: I'm gonna miss you.
- London: I'm gonna miss you too. Thank you so much for coming.
- Girl: You're welcome. Don't get shallow on me.
- London: I promise. Are you kidding me?
The logic says that it's probably something like "don't get mad", but I can't find any proof of that.
The idea is that people outside of town become "shallow"; that is, superficial, dull, phony. The girl is urging the title character to take care not to become that way.
Sense 30.b. for "get, v.", in the OED:
To become... to come to be...
Sense 6 for "shallow, adj.¹ and n.³":
Lacking depth... superficial... Wanting in depth of mind, feeling, or character.
You didn't actually provide enough context. There are certain places particularly associated with shallow people and shallow behavior (as the Anglosphere to the French, America to Britons, and California to Americans and particularly New Yorkers) and presumably London is headed to one of them. "Girl" is expressing some anxiety that London will become similar to the stereotypical resident of X, which saddens her. London tells her "WTF. How can you think that of me?" and then presumably does, in fact, become relatively shallower in "Girl"'s eyes later in the movie for reasons that make sense to a more-mature London and the typical resident of X.
